Should be a drain line somewhere. I don't know where on the LS. On a previous chebby, it was a pipe coming out of the firewall near the AC evaporator assembly. About 1/2 diameter and sticking out maybe 1 inch.
One thing that causes smell is bacteria will often start to grow on the parts within the "air box". With the chebby the dealers had a spray that they sprayed into the air intake for the AC. This killed the bacteria and the smell went away at least until the bacteria took over again. Many members of that website found that spraying a can of Lysol into the air intake did almost as good a job and was way cheaper. I would look for odor free Lysol.
On our LS, if you want to experiment, I would remove the AC intake filter, turn on the AC full blast, NOT Recirculate, and spray some Lysol into the filter airbox. I am only guessing that this is the path the air takes into the cooling section of the LS, but it sounds right. I have not tried this on an LS and can't say it will work, but it does on other cars.
I would also recommend crawling under the car with a strong light and looking for the water outlet and checking to see if it is plugged up. A flexible aquarium brush, pipe cleaner, Chennile(Big pipe cleaner, but prettier), can be used to clear out the outlet. On the Chebby, it was almost a "By feel" only since the outlet was only visible if you got just the right angle of view.
Good Luck,
Jim Henderson